# Finding the next terms of a geometric sequence with whole numbers Online Quiz

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Q 1 - The first three terms of a geometric sequence are 162, 54, and 18. Find the next two terms of this sequence.

### Explanation

Step 1:

The geometric sequence given is 162, 54, 18…

The common ratio is $\frac{54}{162} = \frac{18}{54} = \frac{1}{3}$

Step 2:

The next two terms of the sequence are −

$\frac{18}{3} = 6;\:\frac{6}{3} = 2$.

So the terms are 6 and 2

Q 2 - The first three terms of a geometric sequence are 6, -24, and 96. Find the next two terms of this sequence.

### Explanation

Step 1:

The geometric sequence given is 6, −24, 96…

The common ratio is $\frac{−24}{6} = \frac{96}{−24} = −4$

Step 2:

The next two terms of the sequence are −

96(−4) = −384; −384(−4) = 1536.

So the terms are −384 and 1536

Q 3 - The first three terms of a geometric sequence are 8, 40, and 200. Find the next two terms of this sequence.

### Explanation

Step 1:

The geometric sequence given is 8, 40, 200…

The common ratio is $\frac{40}{8} = \frac{200}{40} = 5$

Step 2:

The next two terms of the sequence are −

200 × 5 = 1000; 1000 × 5 = 5000.

So the terms are 1000 and 5000.

Q 4 - The first three terms of a geometric sequence are 8, -4, and 2. Find the next two terms of this sequence.

### Explanation

Step 1:

The geometric sequence given is 8, −4, 2…

The common ratio is $\frac{−4}{8} = \frac{2}{−4} = \frac{−1}{2}$

Step 2:

The next two terms of the sequence are −

$2 \times \frac{−1}{2} = −1;\: −1 \times \frac{−1}{2} = \frac{1}{2}$.

So the terms are −1 and $\frac{1}{2}$

Q 5 - The first three terms of a geometric sequence are 3, 27, and 243. Find the next two terms of this sequence.

### Explanation

Step 1:

The geometric sequence given is 3, 27, 243…

The common ratio is $\frac{27}{3} = \frac{243}{27} = 9$

Step 2:

The next two terms of the sequence are −

243 × 9 = 2187; 2187 × 9 = 19683.

So the terms are 2187 and 19683

Q 6 - The first three terms of a geometric sequence are 3, 24, and 192. Find the next two terms of this sequence.

### Explanation

Step 1:

The geometric sequence given is 3, 24, 192…

The common ratio is $\frac{24}{3} = \frac{192}{24} = 8$

Step 2:

The next two terms of the sequence are −

192 × 8 = 1536; 1536 × 8 = 12288.

So the terms are 1536 and 12288

Q 7 - The first three terms of a geometric sequence are 4, 16, and 64. Find the next two terms of this sequence.

### Explanation

Step 1:

The geometric sequence given is 4, 16, 64…

The common ratio is $\frac{16}{4} = \frac{64}{16} = 4$

Step 2:

The next two terms of the sequence are −

64 × 4 = 256; 256 × 4 = 1024.

So the terms are 256 and 1024

Q 8 - The first three terms of a geometric sequence are 2, -10, and 50. Find the next two terms of this sequence.

### Explanation

Step 1:

The geometric sequence given is 2, −10, 50…

The common ratio is $\frac{−10}{2} = \frac{50}{−10} = −5$

Step 2:

The next two terms of the sequence are −

50(−5) = −250; −250 × −5 = 1250.

So the terms are −250 and 1250

Q 9 - The first three terms of a geometric sequence are −6, 18, and −54. Find the next two terms of this sequence.

### Explanation

Step 1:

The geometric sequence given is −6, 18, −54…

The common ratio is $\frac{18}{−6} = \frac{−54}{18} = −3$

Step 2:

The next two terms of the sequence are −

−54(−3) = 162; 162 (−3) = 486.

So the terms are 162 and −486

Q 10 - The first three terms of a geometric sequence are 8, -32, and 128. Find the next two terms of this sequence.

### Explanation

Step 1:

The geometric sequence given is 8, −32, 128…

The common ratio is $\frac{−32}{8} = \frac{128}{−32} = −4$

Step 2:

The next two terms of the sequence are −

128(−4) = −512; −512(−4) = 2048.

So the terms are −512 and 2048

finding_next_terms_of_geometric_sequence_with_whole_numbers.htm